In telecommunication networks, modulation is the process of conveying a message signal, for example a digital bit stream or an analog audio signal, inside another signal that may be physically transmitted over a communication channel.
Different types of modulation schemes may be used by a device in a telecommunication network in order to send a digital bit stream over a communication channel. Some known modulation schemes, for example 8-Pulse Amplitude Modulation (8-PAM) or 16-Quadrature Amplitude Modulation (16-QAM), imply first coding the digital bit stream using an alphabet comprising a plurality of different binary sequences, called bit sequences. Hence, when bit sequences are coded on n bits, the alphabet comprises a total number of 2n different bit sequences that may be used for coding the digital bit stream. Each bit sequence of the coded message signal is further mapped, i.e. associated or assigned, to a discrete value, called signal point, which corresponds to a symbol that is embedded in the signal transmitted over the communication channel. Consequently, a mapping between a bit sequence coded on n bits and a signal point allows sending n bits of information by only sending the corresponding one symbol. In such a mapping, 2n different bit sequences are mapped to a plurality of M different signal points, called M-ary constellation. For example, in 8-PAM, 2n bit sequences are mapped to 8 signal points and, in 16-QAM, 2n bit sequences are mapped to 16 signal points.
When the number of bit sequences (2n) is equal to the number of signal points (M), each bit sequence is mapped to one, and only one, signal point. In this case, the mapping is called uniform mapping. When the number of bit sequences (2n) is greater than the number of signal points (M), one or several bit sequences are mapped to one, and only one, signal point. In other words, one set of at least one bit sequence is mapped to one signal point, bit sequences in a set being different from each others and from the bit sequences in the other sets. In this case, the mapping is called non-uniform or quantization mapping. Such a quantization mapping allows mapping more different bit sequences than a uniform mapping with the same number of signal points, increasing thus the performance of the modulation scheme and therefore optimizing the use of the capacity of the communication channel.
In the document “On the application of LDPC codes to arbitrary discrete-memoryless channels”, 2004, A. Bennatan and D. Burshtein used a quantization mapping in a known modulation system, called Bit-Interleaved Coded Modulation-Iterative Decoding (BICM-ID) system. Such a mapping was specifically designed to improve the shaping gain, i.e. reduce the average transmit power, of a transmission on the communication channel. As described in reference to FIG. 1, it implies, firstly, determining, for each signal point x, a number Nb of bit sequences u to be mapped to said each signal point x, the numbers Nb of bit sequences u being distributed according to a discrete Gaussian distribution among the constellation of signal points x, and, secondly, mapping to each signal point x in the constellation, the determined number Nb of bit sequence(s) u, in the natural increasing or respectively decreasing order, all the mapped bit sequences u being different. Such a mapping is called a natural mapping. In the mapping illustrated by FIG. 1 using a 10-PAM modulation scheme, sixteen bit sequences u, coded on four bits are mapped to M=10 signal points x={−9, −7, −5, −3, −1, 1, 3, 5, 7, 9}: 0000 (Nb=1) is mapped to x=−9, 0001 (Nb=1) is mapped to x=−7, 0010 (Nb=1) is mapped to x=−5, 0011 and 0100 (Nb=2) are mapped to x=−3, 0101, 0110, 0111 (Nb=3) are mapped to x=−1, 1000, 1001, 1010 (Nb=3) are mapped to x=1, 1011 and 1100 (Nb=2) are mapped to x=3, 1101 (Nb=1) is mapped to x=5, 1110 (Nb=1) is mapped to x=7 and 1111 (Nb=1) is mapped to x=9.
However, in this solution, the shaping gain is not optimal as bit sequences are mapped to signal points in a natural order.
Today there is no solution to efficiently map a plurality of bit sequences to a plurality of signal points that optimize the shaping gain of a transmission over a communication channel and thus allows improving efficiency of such telecommunication systems.
Today there is a need for an optimized solution that can be easily implemented on the existing communication infrastructures.